Fans of the singer-songwriter Carole King may be happy just to hear a replay of her biggest hits in this West End musical, an efficient re-creation by Marc Bruni of his original Broadway production but with a British cast. While the show is pleasant enough, it struck me as the theatrical equivalent of one of those bland Hollywood biopics in which a local boy or girl makes it to the top of the showbiz ladder.

Douglas McGrath’s book weaves the songs into the story of King’s life. We first see her as a Brooklyn teenager with a passion for music and for her lyric-writing fellow student, Gerry Goffin, quickly identified as a “killer-flirt”.

Working in New York’s factory-like Brill Building, King and Goffin become a prolific songwriting team, get married and bond with their friendly rivals, Cynthia Weil and Barry Mann. But while King craves domestic security, Goffin is a compulsive philanderer and the pair eventually split up, leaving King free to overcome her stage fright and achieve new fame as a solo performer.

It’s good to hear some of the old songs again, such as It Might As Well Rain Until September and The Locomotion, and to be reminded of groups like the Righteous Brothers and the Shirelles. But the attempt to link the songs to the life feels strained, there is little of the ecstasy that drives Sunny Afternoon about Ray Davies and the Kinks. At the end, I felt I still didn’t really know Carole King. She comes across as a shy, well-adjusted woman struggling to reconcile a career with a failing marriage. But, although the audience cheers when she finally ditches Goffin announcing “the girls deserve something better and so do I”, we never discover what drives her on, there’s no mention of her two later marriages and little exploration of how she conquered her inhibitions to become a solo singer.

Beautiful: The Carole King Musical at Aldwych theatre, London. Tristram Kenton for the Guardian

Katie Brayben, lately seen in minor roles in King Charles III and American Psycho, makes the big leap into playing Carole King with admirable skill: she conveys her essential normality, love for music and longing for domestic harmony.

Brayben also suggests a woman who backs nervously into stardom. There’s good support from Alan Morrissey as Goffin, Lorna Want and Ian McIntosh as Weil and Mann, and from the teams who make up 60s groups such as the Drifters and the Shirelles. But the show lacks the drama that some of us still hunger for in a musical.